On chaotic dynamics in transcription factors and the associated effects in differential gene regulation

Integrative Proteomic and Phosphoproteomic Profiling Reveals Molecular Mechanisms of Hypoxic Adaptation in Brandt's Voles (Lasiopodomys brandtii) Brain Tissue

Rapid ascent to high altitudes by unacclimatized individuals significantly increases the risk of brain damage, given the brain's heightened sensitivity to hypoxic conditions. Investigating hypoxia-tolerant animals can provide insights into adaptive mechanisms and guide prevention and treatment of hypoxic-ischemic brain injury. In this study, we exposed Brandt's voles to simulated altitudes (100 m, 3000 m, 5000 m, and 7000 m) for 24 h and performed quantitative proteomic and phosphoproteomic analyses of brain tissue. A total of 3990 proteins and 9125 phosphorylation sites (phospho-sites) were quantified. Differentially expressed (DE) analysis revealed that while protein abundance changes were relatively modest, phosphorylation levels exhibited substantial alterations, suggesting that Brandt's voles rapidly regulate protein structure and function through phosphorylation to maintain cellular homeostasis under acute hypoxia. Clustering analysis showed that most co-expressed proteins exhibited non-monotonic responses with increasing altitude, which were enriched in pathways related to cytokine secretion regulation and glutathione metabolism, contributing to reduced inflammation and oxidative stress. In contrast, most co-expressed phospho-sites showed monotonic changes, with phospho-proteins enriched in glycolysis and vascular smooth muscle contraction regulation. Kinase activity prediction identified nine hypoxia-responsive kinases, four of which belonging to the CAMK family. Immunoblot validated that the changes in CAMK2A activity were consistent with predictions, suggesting that CAMK may play a crucial role in hypoxic response. In conclusion, this work discovered that Brandt's voles may cope with hypoxia through three key strategies: (1) vascular regulation to enhance cerebral blood flow, (2) glycolytic activation to increase energy production, and (3) activation of neuroprotective mechanisms.

The main sources of molecular organization in the cell. Atlas of self-organized and self-regulated dynamic biostructures

One of the most important goals of contemporary biology is to understand the principles of the molecular order underlying the complex dynamic architecture of cells. Here, we present an overview of the main driving forces involved in the cellular molecular complexity and in the emergent functional dynamic structures, spanning from the most basic molecular organization levels to the complex emergent integrative systemic behaviors. First, we address the molecular information processing which is essential in many complex fundamental mechanisms such as the epigenetic memory, alternative splicing, regulation of transcriptional system, and the adequate self-regulatory adaptation to the extracellular environment. Next, we approach the biochemical self-organization, which is central to understand the emergency of metabolic rhythms, circadian oscillations, and spatial traveling waves. Such a complex behavior is also fundamental to understand the temporal compartmentalization of the cellular metabolism and the dynamic regulation of many physiological activities. Numerous examples of biochemical self-organization are considered here, which show that practically all the main physiological processes in the cell exhibit this type of dynamic molecular organization. Finally, we focus on the biochemical self-assembly which, at a primary level of organization, is a basic but important mechanism for the order in the cell allowing biomolecules in a disorganized state to form complex aggregates necessary for a plethora of essential structures and physiological functions. In total, more than 500 references have been compiled in this review. Due to these main sources of order, systemic functional structures emerge in the cell, driving the metabolic functionality towards the biological complexity.

Cell Fate Dynamics Reconstruction Identifies TPT1 and PTPRZ1 Feedback Loops as Master Regulators of Differentiation in Pediatric Glioblastoma-Immune Cell Networks

Pediatric glioblastoma is a complex dynamical disease that is difficult to treat due to its multiple adaptive behaviors driven largely by phenotypic plasticity. Integrated data science and network theory pipelines offer novel approaches to studying glioblastoma cell fate dynamics, particularly phenotypic transitions over time. Here we used various single-cell trajectory inference algorithms to infer signaling dynamics regulating pediatric glioblastoma-immune cell networks. We identified GATA2, PTPRZ1, TPT1, MTRNR2L1/2, OLIG1/2, SOX11, FXYD6, SEZ6L, PDGFRA, EGFR, S100B, WNT, TNF α , and NF-kB as critical transition genes or signals regulating glioblastoma-immune network dynamics, revealing potential clinically relevant targets. Further, we reconstructed glioblastoma cell fate attractors and found complex bifurcation dynamics within glioblastoma phenotypic transitions, suggesting that a causal pattern may be driving glioblastoma evolution and cell fate decision-making. Together, our findings have implications for developing targeted therapies against glioblastoma, and the continued integration of quantitative approaches and artificial intelligence (AI) to understand pediatric glioblastoma tumor-immune interactions.

About the ozone ability in using adaptive chaos to restore a healthy state in the oxygen-ozone adjunct therapy

The action of ozone in medicine is a subject of interest and lively, controversial debates. Its mechanisms of action are still far from fully understood. However, it is possible that ozone triggers a series of dynamics in living organisms related to chaos, multi-stable phenomena, and oscillatory processes. Ozone may be involved in adaptive chaos. Adaptive chaos in health and the reduction of complexity in pathology are interconnected phenomena that describe the functional dynamics of biological systems. Adaptive chaos refers to a state of controlled, complex, and flexible behaviour exhibited by healthy biological systems. It allows for a dynamic balance between order and unpredictability, enabling the system to respond to various internal and external stimuli. In pathological states, the system loses its adaptive chaos, often becoming either too rigid or overly chaotic. This reduction in complexity limits the ability of the system to respond effectively to stimuli, making it prone to dysfunction. This paper addresses the role of ozone in these scenarios.

Phenotypic consequences of logarithmic signaling in MAPK stress response

How cells respond to dynamic environmental changes is crucial for understanding fundamental biological processes and cell physiology. In this study, we developed an experimental and quantitative analytical framework to explore how dynamic stress gradients that change over time regulate cellular volume, signaling activation, and growth phenotypes. Our findings reveal that gradual stress conditions substantially enhance cell growth compared to conventional acute stress. This growth advantage correlates with a minimal reduction in cell volume dependent on the dynamic of stress. We explain the growth phenotype with our finding of a logarithmic signal transduction mechanism in the yeast mitogen-activated protein kinase (MAPK) osmotic stress response pathway. These insights into the interplay between gradual environments, cell volume change, dynamic cell signaling, and growth, advance our understanding of fundamental cellular processes in gradual stress environments.

The chaotic dynamics and behavior of prey-predator interaction: Insights into complex ecological systems and epidemic modeling

This study and the literature have shown that the emergence of chaotic behavior has been attributed mostly to predator-prey and competitive dynamics. This is also observed in pandemics, as well as in cancer models, where deterministic chaos or chaotic dynamics can lead to complex oscillations and nonlinear interactions between cell populations. It is important to note that COVID-19 displays the key characteristics of a chaotic system and is one of the deadliest pandemics in recent history.

Entrainment and multi-stability of the p53 oscillator in human cells

The tumor suppressor p53 responds to cellular stress and activates transcription programs critical for regulating cell fate. DNA damage triggers oscillations in p53 levels with a robust period. Guided by the theory of synchronization and entrainment, we developed a mathematical model and experimental system to test the ability of the p53 oscillator to entrain to external drug pulses of various periods and strengths. We found that the p53 oscillator can be locked and entrained to a wide range of entrainment modes. External periods far from p53's natural oscillations increased the heterogeneity between individual cells whereas stronger inputs reduced it. Single-cell measurements allowed deriving the phase response curves (PRCs) and multiple Arnold tongues of p53. In addition, multi-stability and non-linear behaviors were mathematically predicted and experimentally detected, including mode hopping, period doubling, and chaos. Our work revealed critical dynamical properties of the p53 oscillator and provided insights into understanding and controlling it. A record of this paper's transparent peer review process is included in the supplemental information.

Predicting bacterial transcription factor binding sites through machine learning and structural characterization based on DNA duplex stability

Transcriptional factors (TFs) in bacteria play a crucial role in gene regulation by binding to specific DNA sequences, thereby assisting in the activation or repression of genes. Despite their central role, deciphering shape recognition of bacterial TFs-DNA interactions remains an intricate challenge. A deeper understanding of DNA secondary structures could greatly enhance our knowledge of how TFs recognize and interact with DNA, thereby elucidating their biological function. In this study, we employed machine learning algorithms to predict transcription factor binding sites (TFBS) and classify them as directed-repeat (DR) or inverted-repeat (IR). To accomplish this, we divided the set of TFBS nucleotide sequences by size, ranging from 8 to 20 base pairs, and converted them into thermodynamic data known as DNA duplex stability (DDS). Our results demonstrate that the Random Forest algorithm accurately predicts TFBS with an average accuracy of over 82% and effectively distinguishes between IR and DR with an accuracy of 89%. Interestingly, upon converting the base pairs of several TFBS-IR into DDS values, we observed a symmetric profile typical of the palindromic structure associated with these architectures. This study presents a novel TFBS prediction model based on a DDS characteristic that may indicate how respective proteins interact with base pairs, thus providing insights into molecular mechanisms underlying bacterial TFs-DNA interaction.

From resonance to chaos by modulating spatiotemporal patterns through a synthetic optogenetic oscillator

Oscillations are a recurrent phenomenon in biological systems across scales, but deciphering their fundamental principles is very challenging. Here, we tackle this challenge by redesigning the wellcharacterised synthetic oscillator known as "repressilator" in Escherichia coli and controlling it using optogenetics, creating the "optoscillator". Bacterial colonies manifest oscillations as spatial ring patterns. When we apply periodic light pulses, the optoscillator behaves as a forced oscillator and we systematically investigate the properties of the rings under various light conditions. Combining experiments with mathematical modeling, we demonstrate that this simple oscillatory circuit can generate complex dynamics that are transformed into distinct spatial patterns. We report the observation of synchronisation, resonance, subharmonic resonance and period doubling. Furthermore, we present evidence of a chaotic regime. This work highlights the intricate spatiotemporal patterns accessible by synthetic oscillators and underscores the potential of our approach in revealing fundamental principles of biological oscillations.

Synthetic gene circuit evolution: Insights and opportunities at the mid-scale

Directed evolution focuses on optimizing single genetic components for predefined engineering goals by artificial mutagenesis and selection. In contrast, experimental evolution studies the adaptation of entire genomes in serially propagated cell populations, to provide an experimental basis for evolutionary theory. There is a relatively unexplored gap at the middle ground between these two techniques, to evolve in vivo entire synthetic gene circuits with nontrivial dynamic function instead of single parts or whole genomes. We discuss the requirements for such mid-scale evolution, with hypothetical examples for evolving synthetic gene circuits by appropriate selection and targeted shuffling of a seed set of genetic components in vivo. Implementing similar methods should aid the rapid generation, functionalization, and optimization of synthetic gene circuits in various organisms and environments, accelerating both the development of biomedical and technological applications and the understanding of principles guiding regulatory network evolution.

Dynamical analysis of a periodically forced chaotic chemical oscillator

We present a comprehensive dynamical analysis of a chaotic chemical model referred to as the autocatalator, when subject to a periodic administration of one substrate. Our investigation encompasses the dynamical characterization of both unforced and forced systems utilizing isospikes and largest Lyapunov exponents-based parameter planes, bifurcation diagrams, and analysis of complex oscillations. Additionally, we present a phase diagram showing the effect of the period and amplitude of the forcing signal on the system's behavior. Furthermore, we show how the landscapes of parameter planes are altered in response to forcing application. This analysis contributes to a deeper understanding of the intricate dynamics induced by the periodic forcing of a chaotic system.

Viewing cancer as a chaotic ‘information processing system’

The effort to define life encompasses a wide range of disciplines, from biology and physics to spirituality. Traditionally, replies were restricted to specialized specialties, resulting in disjointed solutions. Cancer research has mostly concentrated on genetic and cellular factors. This essay aims to reframe the way we think about cancer by looking at it through the perspective of information processing. It investigates the cybernetic component of life, perceiving it as a unified system of information processing at all scales. Stem cell research reveals their complex heterogeneity and flexibility, which are critical for tissue repair and development. Initially thought to be harmful, chaotic gene expression is now acknowledged to provide cellular flexibility. Using chaos to improve adaptation contrasts with the unpredictability of evolution, showcasing the system's ability to learn and adapt. Creativity, disorder and chaos interact, opening up new avenues for new ideas. This viewpoint opposes the gene‐centric view of cancer and highlights the importance of understanding biological processes beyond genetic reductionism. The essay finishes by pushing for a paradigm change towards seeing cancer as an informational process rather than just a hereditary disease and encouraging a better knowledge of the information processing capabilities of cellular life.

Cellular heterogeneity in TNF/TNFR1 signalling: live cell imaging of cell fate decisions in single cells

Cellular responses to TNF are inherently heterogeneous within an isogenic cell population and across different cell types. TNF promotes cell survival by activating pro-inflammatory NF-κB and MAPK signalling pathways but may also trigger apoptosis and necroptosis. Following TNF stimulation, the fate of individual cells is governed by the balance of pro-survival and pro-apoptotic signalling pathways. To elucidate the molecular mechanisms driving heterogenous responses to TNF, quantifying TNF/TNFR1 signalling at the single-cell level is crucial. Fluorescence live-cell imaging techniques offer real-time, dynamic insights into molecular processes in single cells, allowing for detection of rapid and transient changes, as well as identification of subpopulations, that are likely to be missed with traditional endpoint assays. Whilst fluorescence live-cell imaging has been employed extensively to investigate TNF-induced inflammation and TNF-induced cell death, it has been underutilised in studying the role of TNF/TNFR1 signalling pathway crosstalk in guiding cell-fate decisions in single cells. Here, we outline the various opportunities for pathway crosstalk during TNF/TNFR1 signalling and how these interactions may govern heterogenous responses to TNF. We also advocate for the use of live-cell imaging techniques to elucidate the molecular processes driving cell-to-cell variability in single cells. Understanding and overcoming cellular heterogeneity in response to TNF and modulators of the TNF/TNFR1 signalling pathway could lead to the development of targeted therapies for various diseases associated with aberrant TNF/TNFR1 signalling, such as rheumatoid arthritis, metabolic syndrome, and cancer.

Chaos in a bacterial stress response

Cellular responses to environmental changes are often highly heterogeneous and exhibit seemingly random dynamics. The astonishing insight of chaos theory is that such unpredictable patterns can, in principle, arise without the need for any random processes, i.e., purely deterministically without noise. However, while chaos is well understood in mathematics and physics, its role in cell biology remains unclear because the complexity and noisiness of biological systems make testing difficult. Here, we show that chaos explains the heterogeneous response of Escherichia coli cells to oxidative stress. We developed a theoretical model of the gene expression dynamics and demonstrate that chaotic behavior arises from rapid molecular feedbacks that are coupled with cell growth dynamics and cell-cell interactions. Based on theoretical predictions, we then designed single-cell experiments to show we can shift gene expression from periodic oscillations to chaos on demand. Our work suggests that chaotic gene regulation can be employed by cell populations to generate strong and variable responses to changing environments.

Phenotypic consequences of logarithmic signaling in MAPK stress response

How cells respond to dynamic environmental changes is crucial for understanding fundamental biological processes and cell physiology. In this study, we developed an experimental and quantitative analytical framework to explore how dynamic stress gradients that change over time regulate cellular volume, signaling activation, and growth phenotypes. Our findings reveal that gradual stress conditions substantially enhance cell growth compared to conventional acute stress. This growth advantage correlates with a minimal reduction in cell volume dependent on the dynamic of stress. We explain the growth phenotype with our finding of a logarithmic signal transduction mechanism in the yeast Mitogen-Activated Protein Kinase (MAPK) osmotic stress response pathway. These insights into the interplay between gradual environments, cell volume change, dynamic cell signaling, and growth, advance our understanding of fundamental cellular processes in gradual stress environments.

Deep-learning-assisted Sort-Seq enables high-throughput profiling of gene expression characteristics with high precision

Owing to the nondeterministic and nonlinear nature of gene expression, the steady-state intracellular protein abundance of a clonal population forms a distribution. The characteristics of this distribution, including expression strength and noise, are closely related to cellular behavior. However, quantitative description of these characteristics has so far relied on arrayed methods, which are time-consuming and labor-intensive. To address this issue, we propose a deep-learning-assisted Sort-Seq approach (dSort-Seq) in this work, enabling high-throughput profiling of expression properties with high precision. We demonstrated the validity of dSort-Seq for large-scale assaying of the dose-response relationships of biosensors. In addition, we comprehensively investigated the contribution of transcription and translation to noise production in Escherichia coli, from which we found that the expression noise is strongly coupled with the mean expression level. We also found that the transcriptional interference caused by overlapping RpoD-binding sites contributes to noise production, which suggested the existence of a simple and feasible noise control strategy in E. coli.

Periodicity, mixed-mode oscillations, and multiple timescales in a phosphoinositide-Rho GTPase network

While rhythmic contractile behavior is commonly observed at the cellular cortex, the primary focus has been on excitable or periodic events described by simple activator-delayed inhibitor mechanisms. We show that Rho GTPase activation in nocodazole-treated mitotic cells exhibits both simple oscillations and complex mixed-mode oscillations. Rho oscillations with a 20- to 30-s period are regulated by phosphatidylinositol (3,4,5)-trisphosphate (PIP3) via an activator-delayed inhibitor mechanism, while a slow reaction with period of minutes is regulated by phosphatidylinositol 4-kinase via an activator-substrate depletion mechanism. Conversion from simple to complex oscillations can be induced by modulating PIP3 metabolism or altering membrane contact site protein E-Syt1. PTEN depletion results in a period-doubling intermediate, which, like mixed-mode oscillations, is an intermediate state toward chaos. In sum, this system operates at the edge of chaos. Small changes in phosphoinositide metabolism can confer cells with the flexibility to rapidly enter ordered states with different periodicities.

Are physiological oscillations physiological?

Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we take a systems approach to argue that oscillations play critical physiological roles, such as enabling systems to avoid desensitization, to avoid chronically high and therefore toxic levels of chemicals, and to become more resistant to noise. Oscillation also enables complex physiological systems to reconcile incompatible conditions such as oxidation and reduction, by cycling between them, and to synchronize the oscillations of many small units into one large effect. In pancreatic β-cells, glycolytic oscillations synchronize with calcium and mitochondrial oscillations to drive pulsatile insulin release, critical for liver regulation of glucose. In addition, oscillation can keep biological time, essential for embryonic development in promoting cell diversity and pattern formation. The functional importance of oscillatory processes requires a re-thinking of the traditional doctrine of homeostasis, holding that physiological quantities are maintained at constant equilibrium values, a view that has largely failed in the clinic. A more dynamic approach will initiate a paradigm shift in our view of health and disease. A deeper look into the mechanisms that create, sustain and abolish oscillatory processes requires the language of nonlinear dynamics, well beyond the linearization techniques of equilibrium control theory. Nonlinear dynamics enables us to identify oscillatory ('pacemaking') mechanisms at the cellular, tissue and system levels.

Coupled oscillator cooperativity as a control mechanism in chronobiology

Control of dynamical processes is vital for maintaining correct cell regulation and cell-fate decisions. Numerous regulatory networks show oscillatory behavior; however, our knowledge of how one oscillator behaves when stimulated by two or more external oscillatory signals is still missing. We explore this problem by constructing a synthetic oscillatory system in yeast and stimulate it with two external oscillatory signals. Letting model verification and prediction operate in a tight interplay with experimental observations, we find that stimulation with two external signals expands the plateau of entrainment and reduces the fluctuations of oscillations. Furthermore, by adjusting the phase differences of external signals, one can control the amplitude of oscillations, which is understood through the signal delay of the unperturbed oscillatory network. With this we reveal a direct amplitude dependency of downstream gene transcription. Taken together, these results suggest a new path to control oscillatory systems by coupled oscillator cooperativity.

Robust morphogenesis by chaotic dynamics

This research illustrates that complex dynamics of gene products enable the creation of any prescribed cellular differentiation patterns. These complex dynamics can take the form of chaotic, stochastic, or noisy chaotic dynamics. Based on this outcome and previous research, it is established that a generic open chemical reactor can generate an exceptionally large number of different cellular patterns. The mechanism of pattern generation is robust under perturbations and it is based on a combination of Turing's machines, Turing instability and L. Wolpert's gradients. These results can help us to explain the formidable adaptive capacities of biochemical systems.

Effect of seabuckthorn seed protein and its arginine-enriched peptides on combating memory impairment in mice

The current study characterized the combating memory impairment effect of seabuckthorn seed protein (SSP) and the arginine (Arg)-enriched peptides (SSPP) on d-galactose-induced brain aging in mice. The Arg content in SSP and SSPP were 10.11 and 17.82 g/100 g, respectively. Seven Arg peptides (Ile/Leu-Arg, Arg-Glu, Asp-Arg-Pro, Arg-Try-Ala, Glu-Arg-Ser, Val-Gly-Arg-Pro, and Lys-Thr-Glu-Arg) were identified from SSPP. The animal experiments of the Morris water maze and the step-down test indicated that the oral administration of SSP (0.25, 0.5, 1.0 mg/g·d) and SSPP (0.25, 0.5, 1.0 mg/g·d) significantly (p < 0.05) reversed the learning and memory impairment symptoms. The activation of endothelial nitric oxide (NO) synthase and neuronal NO synthase were increased, and inducible NO synthase decreased after SSP and SSPP in the hippocampus compared to the model group, with the SSPP being quite effective. Moreover, the treatment significantly exhibited the ability to normalize the serum inflammatory cytokine levels (NF-ĸB, TNF-α, IL-6) and suppress the Arg-inducible nitric oxide (Arg-iNO) pathway. Therefore, SSP and SSPP ingestion reversed the behavioral learning and memory impairment symptoms possibly associated with the anti-inflammation and Arg-iNO pathway. Consumption of SSP and SSPP diets can be beneficial to memory impairment.

Embracing complexity in sepsis

Sepsis involves the dynamic interplay between a pathogen, the host response, the failure of organ systems, medical interventions and a myriad of other factors. This together results in a complex, dynamic and dysregulated state that has remained ungovernable thus far. While it is generally accepted that sepsis is very complex indeed, the concepts, approaches and methods that are necessary to understand this complexity remain underappreciated. In this perspective we view sepsis through the lens of complexity theory. We describe the concepts that support viewing sepsis as a state of a highly complex, non-linear and spatio-dynamic system. We argue that methods from the field of complex systems are pivotal for a fuller understanding of sepsis, and we highlight the progress that has been made over the last decades in this respect. Still, despite these considerable advancements, methods like computational modelling and network-based analyses continue to fly under the general scientific radar. We discuss what barriers contribute to this disconnect, and what we can do to embrace complexity with regards to measurements, research approaches and clinical applications. Specifically, we advocate a focus on longitudinal, more continuous biological data collection in sepsis. Understanding the complexity of sepsis will require a huge multidisciplinary effort, in which computational approaches derived from complex systems science must be supported by, and integrated with, biological data. Such integration could finetune computational models, guide validation experiments, and identify key pathways that could be targeted to modulate the system to the benefit of the host. We offer an example for immunological predictive modelling, which may inform agile trials that could be adjusted throughout the trajectory of disease. Overall, we argue that we should expand our current mental frameworks of sepsis, and embrace nonlinear, system-based thinking in order to move the field forward.

Boolean modeling reveals that cyclic attractors in macrophage polarization serve as reservoirs of states to balance external perturbations from the tumor microenvironment

Cyclic attractors generated from Boolean models may explain the adaptability of a cell in response to a dynamical complex tumor microenvironment. In contrast to this idea, we postulate that cyclic attractors in certain cases could be a systemic mechanism to face the perturbations coming from the environment. To justify our conjecture, we present a dynamic analysis of a highly curated transcriptional regulatory network of macrophages constrained into a cancer microenvironment. We observed that when M1-associated transcription factors (STAT1 or NF-κB) are perturbed and the microenvironment balances to a hyper-inflammation condition, cycle attractors activate genes whose signals counteract this effect implicated in tissue damage. The same behavior happens when the M2-associated transcription factors are disturbed (STAT3 or STAT6); cycle attractors will prevent a hyper-regulation scenario implicated in providing a suitable environment for tumor growth. Therefore, here we propose that cyclic macrophage phenotypes can serve as a reservoir for balancing the phenotypes when a specific phenotype-based transcription factor is perturbed in the regulatory network of macrophages. We consider that cyclic attractors should not be simply ignored, but it is necessary to carefully evaluate their biological importance. In this work, we suggest one conjecture: the cyclic attractors can serve as a reservoir to balance the inflammatory/regulatory response of the network under external perturbations.

NF-kB in Signaling Patterns and Its Temporal Dynamics Encode/Decode Human Diseases

Defects in signaling pathways are the root cause of many disorders. These malformations come in a wide variety of types, and their causes are also very diverse. Some of these flaws can be brought on by pathogenic organisms and viruses, many of which can obstruct signaling processes. Other illnesses are linked to malfunctions in the way that cell signaling pathways work. When thinking about how errors in signaling pathways might cause disease, the idea of signalosome remodeling is helpful. The signalosome may be conveniently divided into two types of defects: phenotypic remodeling and genotypic remodeling. The majority of significant illnesses that affect people, including high blood pressure, heart disease, diabetes, and many types of mental illness, appear to be caused by minute phenotypic changes in signaling pathways. Such phenotypic remodeling modifies cell behavior and subverts normal cellular processes, resulting in illness. There has not been much progress in creating efficient therapies since it has been challenging to definitively confirm this connection between signalosome remodeling and illness. The considerable redundancy included into cell signaling systems presents several potential for developing novel treatments for various disease conditions. One of the most important pathways, NF-κB, controls several aspects of innate and adaptive immune responses, is a key modulator of inflammatory reactions, and has been widely studied both from experimental and theoretical perspectives. NF-κB contributes to the control of inflammasomes and stimulates the expression of a number of pro-inflammatory genes, including those that produce cytokines and chemokines. Additionally, NF-κB is essential for controlling innate immune cells and inflammatory T cells' survival, activation, and differentiation. As a result, aberrant NF-κB activation plays a role in the pathogenesis of several inflammatory illnesses. The activation and function of NF-κB in relation to inflammatory illnesses was covered here, and the advancement of treatment approaches based on NF-κB inhibition will be highlighted. This review presents the temporal behavior of NF-κB and its potential relevance in different human diseases which will be helpful not only for theoretical but also for experimental perspectives.

Enhanced DNA repair through droplet formation and p53 oscillations

Living organisms are constantly exposed to DNA damage, and optimal repair is therefore crucial. A characteristic hallmark of the response is the formation of sub-compartments around the site of damage, known as foci. Following multiple DNA breaks, the transcription factor p53 exhibits oscillations in its nuclear concentration, but how this dynamics can affect the repair remains unknown. Here, we formulate a theory for foci formation through droplet condensation and discover how oscillations in p53, with its specific periodicity and amplitude, optimize the repair process by preventing Ostwald ripening and distributing protein material in space and time. Based on the theory predictions, we reveal experimentally that the oscillatory dynamics of p53 does enhance the repair efficiency. These results connect the dynamical signaling of p53 with the microscopic repair process and create a new paradigm for the interplay of complex dynamics and phase transitions in biology.

New 4D and 3D models of chaotic systems developed from the dynamic behavior of nuclear reactors

The complex, highly nonlinear dynamic behavior of nuclear reactors can be captured qualitatively by novel four-dimensional (that is, fourth order) and three-dimensional (that is, third order) models of chaotic systems and analyzed with Lyapunov spectra, bifurcation diagrams, and phase diagrams. The chaotic systems exhibit a rich variety of bifurcation phenomena, including the periodic-doubling route to chaos, reverse bifurcations, anti-monotonicity, and merging chaos. The offset boosting method, which relocates the attractor's basin of attraction in any direction, is demonstrated in these chaotic systems. Both constant parameters and periodic functions are seen in offset boosting phenomena, yielding chaotic attractors with controlled mean values and coexisting attractors.

A common pathway to cancer: Oncogenic mutations abolish p53 oscillations

The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly, they exhibit a mixed pattern of interactions in tumors, such as co-occurrence, mutual exclusivity, and paradoxically, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics, we employ Hopf bifurcation analysis to show that these alterations have a common mode of action, to abolish the oscillatory competence of p53, thereby, we suggest, impairing its tumor suppressive function. In this analysis, diverse genetic alterations, widely associated with human cancers clinically, have a unified mechanistic explanation of their role in oncogenesis.

Network design principle for robust oscillatory behaviors with respect to biological noise

Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus, a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive autoregulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive autoregulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive autoregulation—improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.

Brain-inspired chaotic backpropagation for MLP

Backpropagation (BP) algorithm is one of the most basic learning algorithms in deep learning. Although BP has been widely used, it still suffers from the problem of easily falling into the local minima due to its gradient dynamics. Inspired by the fact that the learning of real brains may exploit chaotic dynamics, we propose the chaotic backpropagation (CBP) algorithm by integrating the intrinsic chaos of real neurons into BP. By validating on multiple datasets (e.g. cifar10), we show that, for multilayer perception (MLP), CBP has significantly better abilities than those of BP and its variants in terms of optimization and generalization from both computational and theoretical viewpoints. Actually, CBP can be regarded as a general form of BP with global searching ability inspired by the chaotic learning process in the brain. Therefore, CBP not only has the potential of complementing or replacing BP in deep learning practice, but also provides a new way for understanding the learning process of the real brain.

Dissecting cell fate dynamics in pediatric glioblastoma through the lens of complex systems and cellular cybernetics

Cancers are complex dynamic ecosystems. Reductionist approaches to science are inadequate in characterizing their self-organized patterns and collective emergent behaviors. Since current approaches to single-cell analysis in cancer systems rely primarily on single time-point multiomics, many of the temporal features and causal adaptive behaviors in cancer dynamics are vastly ignored. As such, tools and concepts from the interdisciplinary paradigm of complex systems theory are introduced herein to decode the cellular cybernetics of cancer differentiation dynamics and behavioral patterns. An intuition for the attractors and complex networks underlying cancer processes such as cell fate decision-making, multiscale pattern formation systems, and epigenetic state-transitions is developed. The applications of complex systems physics in paving targeted therapies and causal pattern discovery in precision oncology are discussed. Pediatric high-grade gliomas are discussed as a model-system to demonstrate that cancers are complex adaptive systems, in which the emergence and selection of heterogeneous cellular states and phenotypic plasticity are driven by complex multiscale network dynamics. In specific, pediatric glioblastoma (GBM) is used as a proof-of-concept model to illustrate the applications of the complex systems framework in understanding GBM cell fate decisions and decoding their adaptive cellular dynamics. The scope of these tools in forecasting cancer cell fate dynamics in the emerging field of computational oncology and patient-centered systems medicine is highlighted.

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

Temperature Controls Onset and Period of NF-κB Oscillations and can Lead to Chaotic Dynamics

The transcription factor NF-κB plays a vital role in the control of the immune system, and following stimulation with TNF-α its nuclear concentration shows oscillatory behaviour. How environmental factors, in particular temperature, can control the oscillations and thereby affect gene stimulation is still remains to be resolved question. In this work, we reveal that the period of the oscillations decreases with increasing temperature. We investigate this using a mathematical model, and by applying results from statistical physics, we introduce temperature dependency to all rates, resulting in a remarkable correspondence between model and experiments. Our model predicts how temperature affects downstream protein production and find a crossover, where high affinity genes upregulates at high temperatures. Finally, we show how or that oscillatory temperatures can entrain NF-κB oscillations and lead to chaotic dynamics presenting a simple path to chaotic conditions in cellular biology.

The onset of dissipative chaos driven by nonequilibrium conditions

Dissipative chaos appears widely in various nonequilibrium systems; however, it is not clear how dissipative chaos originates from nonequilibrium. We discuss a framework based on the potential-flux approach to study chaos from the perspective of nonequilibrium dynamics. In this framework, chaotic systems possess a wide basin on the potential landscape, in which the rotational flux dominates the system dynamics, and chaos occurs with the appearance of this basin. In contrast, the probability flux is particularly associated with the detailed balance-breaking in nonequilibrium systems. This implies that the appearance of dissipative chaos is driven by nonequilibrium conditions.

Neuromechanical modulation of transmembrane voltage in a model of a nerve

Despite substantial evidence that mechanical variables play a crucial role in transmembrane voltage regulation, most research efforts focus mostly on the nerve cell's biochemical or electrophysiological activities. We propose an electromechanical model of a nerve in order to advance our understanding of how mechanical forces and thermodynamics also regulate neural electrical activities. We explore the spatiotemporal dynamics of the transmembrane potential using the proposed nonlinear model with a sinusoid as the initial transmembrane potential and periodic boundary conditions. The localized wave from our numerical simulation and transmembrane potentials in nerves are solitary and show the three stages of action potential (depolarization, repolarization, and hyperpolarization), as well as threshold and saturation effects. We show that the mechanical properties of membranes affect the localization of the transmembrane potential. According to simulation data, mechanical pulses of sufficient magnitude can modulate a transmembrane voltage. The current model could be used to describe the dynamics of a transmembrane potential modulated by sound. Mechanical perturbations that modulate an electrical signal have a lot of clinical potential for treating pain and other neurological diseases.

Inferred expression regulator activities suggest genes mediating cardiometabolic genetic signals

Expression QTL (eQTL) analyses have suggested many genes mediating genome-wide association study (GWAS) signals but most GWAS signals still lack compelling explanatory genes. We have leveraged an adipose-specific gene regulatory network to infer expression regulator activities and phenotypic master regulators (MRs), which were used to detect activity QTLs (aQTLs) at cardiometabolic trait GWAS loci. Regulator activities were inferred with the VIPER algorithm that integrates enrichment of expected expression changes among a regulator's target genes with confidence in their regulator-target network interactions and target overlap between different regulators (i.e., pleiotropy). Phenotypic MRs were identified as those regulators whose activities were most important in predicting their respective phenotypes using random forest modeling. While eQTLs were typically more significant than aQTLs in cis, the opposite was true among candidate MRs in trans. Several GWAS loci colocalized with MR trans-eQTLs/aQTLs in the absence of colocalized cis-QTLs. Intriguingly, at the 1p36.1 BMI GWAS locus the EPHB2 cis-aQTL was stronger than its cis-eQTL and colocalized with the GWAS signal and 35 BMI MR trans-aQTLs, suggesting the GWAS signal may be mediated by effects on EPHB2 activity and its downstream effects on a network of BMI MRs. These MR and aQTL analyses represent systems genetic methods that may be broadly applied to supplement standard eQTL analyses for suggesting molecular effects mediating GWAS signals.

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

A tale of two rhythms: Locked clocks and chaos in biology

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

Robust, coherent, and synchronized circadian clock-controlled oscillations along Anabaena filaments

Circadian clocks display remarkable reliability despite significant stochasticity in biomolecular reactions. We study the dynamics of a circadian clock-controlled gene at the individual cell level in Anabaena sp. PCC 7120, a multicellular filamentous cyanobacterium. We found significant synchronization and spatial coherence along filaments, clock coupling due to cell-cell communication, and gating of the cell cycle. Furthermore, we observed low-amplitude circadian oscillatory transcription of kai genes encoding the post-transcriptional core oscillatory circuit and high-amplitude oscillations of rpaA coding for the master regulator transducing the core clock output. Transcriptional oscillations of rpaA suggest an additional level of regulation. A stochastic one-dimensional toy model of coupled clock cores and their phosphorylation states shows that demographic noise can seed stochastic oscillations outside the region where deterministic limit cycles with circadian periods occur. The model reproduces the observed spatio-temporal coherence along filaments and provides a robust description of coupled circadian clocks in a multicellular organism.

A design principle for posttranslational chaotic oscillators

Chaos behavior has been observed in various cellular and molecular processes. Here, we modeled reversible phosphorylation dynamics to elucidate a design principle for autonomous chaos generation that may arise from generic enzymatic reactions. A comprehensive parameter search demonstrated that the reaction system composed of a set of kinases and phosphatases and two substrates with two modification sites exhibits chaos behavior. All reactions are described according to the Michaelis-Menten reaction scheme without exotic functions being applied to enzymes and substrates. Clustering analysis of parameter sets that can generate chaos behavior revealed the existence of motif structures. These chaos motifs allow the two-substrate species to interact via enzyme availability and constrain the two substrates' dynamic changes in phosphorylation status so that they occur at different timescales. This chaos motif structure is found in several enzymatic reactions, suggesting that chaos behavior may underlie cellular autonomy in a variety of biochemical systems.

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Two substrates with reversible two-site phosphorylation can exhibit chaos behavior

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The chaos does not require autocatalysis or allosteric regulation of enzymes

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The chaos is a result of the coupling of two substrates via enzyme availability

Cellular sociology regulates the hierarchical spatial patterning and organization of cells in organisms

Advances in single-cell biotechnology have increasingly revealed interactions of cells with their surroundings, suggesting a cellular society at the microscale. Similarities between cells and humans across multiple hierarchical levels have quantitative inference potential for reaching insights about phenotypic interactions that lead to morphological forms across multiple scales of cellular organization, namely cells, tissues and organs. Here, the functional and structural comparisons between how cells and individuals fundamentally socialize to give rise to the spatial organization are investigated. Integrative experimental cell interaction assays and computational predictive methods shape the understanding of societal perspective in the determination of the cellular interactions that create spatially coordinated forms in biological systems. Emerging quantifiable models from a simpler biological microworld such as bacterial interactions and single-cell organisms are explored, providing a route to model spatio-temporal patterning of morphological structures in humans. This analogical reasoning framework sheds light on structural patterning principles as a result of biological interactions across the cellular scale and up.

Considering Interim Interventions to Control COVID-19 Associated Morbidity and Mortality-Perspectives

Aims and objectives: The pandemic of COVID-19 is evolving worldwide, and it is associated with high mortality and morbidity. There is a growing need to discuss the elements of a coordinated strategy to control the spread and mitigate the severity of COVID-19. H1N1 and Streptococcus pneumonia vaccines are available. The current analysis was performed to analyze the severity of COVID-19 and influenza (H1N1) vaccination in adults ≥ 65. Also, to correlate the lower respiratory tract infections (LRIs), and influenza attributable to the lower respiratory tract infections' incidence with Covid-19 mortality. Evolutionarily influenza is close in resemblance to SARS-CoV-2 viruses and shares some common epitopes and mechanisms.

Methods: Recent influenza vaccination data of 34 countries from OECD and other publications were correlated with COVID-19 mortality from worldometer data. LRIs attributable to influenza and streptococcus pneumonia were correlated with COVID-19 mortality. Specifically, influenza-attributable LRI incidence data of various countries (n = 182) was correlated with COVID-19 death by linear regression and receiver operating characteristic (ROC) curve analyzes. In a logistic regression model, population density and influenza LRI incidence were correlated with COVID-19 mortality.

Results: There is a correlation between COVID-19-related mortality, morbidity, and case incidence and the status of influenza vaccination, which appears protective. The tendency of correlation is increasingly highlighted as the pandemic is evolving. In countries where influenza immunization is less common, there is a correlation between LRIs and influenza attributable to LRI incidence and COVID-19 severity, which is beneficial. ROC curve showed an area under the curve of 0.86 (CI 0.78 to 0.944, P < 0.0001) to predict COVID-19 mortality >150/million and a decreasing trend of influenza LRI episodes. To predict COVID-19 mortality of >200/million population, the odds ratio for influenza incidence/100,000 was −1.86 (CI −2.75 to −0.96, P < 0.0001). To predict the parameter Covid-19 mortality/influenza LRI episodes^*1000>1000, the influenza parameter had an odd's ratio of −3.83 (CI −5.98 to −1.67), and an AUC of 0.94.

Conclusion: Influenza (H1N1) vaccination can be used as an interim measure to mitigate the severity of COVID-19 in the general population. In appropriate high-risk circumstances, Streptococcus pneumonia vaccination would also be an adjunct strategy, especially in countries with a lower incidence of LRIs.

Concerted localization-resets precede YAP-dependent transcription

Yes-associated protein 1 (YAP) is a transcriptional regulator with critical roles in mechanotransduction, organ size control, and regeneration. Here, using advanced tools for real-time visualization of native YAP and target gene transcription dynamics, we show that a cycle of fast exodus of nuclear YAP to the cytoplasm followed by fast reentry to the nucleus ("localization-resets") activates YAP target genes. These "resets" are induced by calcium signaling, modulation of actomyosin contractility, or mitosis. Using nascent-transcription reporter knock-ins of YAP target genes, we show a strict association between these resets and downstream transcription. Oncogenically-transformed cell lines lack localization-resets and instead show dramatically elevated rates of nucleocytoplasmic shuttling of YAP, suggesting an escape from compartmentalization-based control. The single-cell localization and transcription traces suggest that YAP activity is not a simple linear function of nuclear enrichment and point to a model of transcriptional activation based on nucleocytoplasmic exchange properties of YAP.

Short Residence Times of DNA-Bound Transcription Factors Can Reduce Gene Expression Noise and Increase the Transmission of Information in a Gene Regulation System

Gene expression noise is not just ubiquitous but also variable, and we still do not understand some of the most elementary factors that affect it. Among them is the residence time of a transcription factor (TF) on DNA, the mean time that a DNA-bound TF remains bound. Here, we use a stochastic model of transcriptional regulation to study how residence time affects the gene expression noise that arises when a TF induces gene expression. We find that the effect of residence time on gene expression noise depends on the TF’s concentration and its affinity to DNA, which determine the level of induction of the gene. At high levels of induction, residence time has no effect on gene expression noise. However, as the level of induction decreases, short residence times reduce gene expression noise. The reason is that fast on-off TF binding dynamics prevent long periods where proteins are predominantly synthesized or degraded, which can cause excessive fluctuations in gene expression. As a consequence, short residence times can help a gene regulation system acquire information about the cellular environment it operates in. Our predictions are consistent with the observation that experimentally measured residence times are usually modest and lie between seconds to minutes.

Reverse engineering directed gene regulatory networks from transcriptomics and proteomics data of biomining bacterial communities with approximate Bayesian computation and steady-state signalling simulations

BACKGROUND

Network inference is an important aim of systems biology. It enables the transformation of OMICs datasets into biological knowledge. It consists of reverse engineering gene regulatory networks from OMICs data, such as RNAseq or mass spectrometry-based proteomics data, through computational methods. This approach allows to identify signalling pathways involved in specific biological functions. The ability to infer causality in gene regulatory networks, in addition to correlation, is crucial for several modelling approaches and allows targeted control in biotechnology applications.

METHODS

We performed simulations according to the approximate Bayesian computation method, where the core model consisted of a steady-state simulation algorithm used to study gene regulatory networks in systems for which a limited level of details is available. The simulations outcome was compared to experimentally measured transcriptomics and proteomics data through approximate Bayesian computation.

RESULTS

The structure of small gene regulatory networks responsible for the regulation of biological functions involved in biomining were inferred from multi OMICs data of mixed bacterial cultures. Several causal inter- and intraspecies interactions were inferred between genes coding for proteins involved in the biomining process, such as heavy metal transport, DNA damage, replication and repair, and membrane biogenesis. The method also provided indications for the role of several uncharacterized proteins by the inferred connection in their network context.

CONCLUSIONS

The combination of fast algorithms with high-performance computing allowed the simulation of a multitude of gene regulatory networks and their comparison to experimentally measured OMICs data through approximate Bayesian computation, enabling the probabilistic inference of causality in gene regulatory networks of a multispecies bacterial system involved in biomining without need of single-cell or multiple perturbation experiments. This information can be used to influence biological functions and control specific processes in biotechnology applications.

A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available.

Inferring Leading Interactions in the p53/Mdm2/Mdmx Circuit through Live-Cell Imaging and Modeling

The tumor-suppressive transcription factor p53 is a master regulator of stress responses. In non-stressed conditions, p53 is maintained at low levels by the ubiquitin ligase Mdm2 and its binding partner Mdmx. Mdmx depletion leads to a biphasic p53 response, with an initial post-mitotic pulse followed by oscillations. The mechanism underlying this dynamical behavior is unknown. Two different roles for Mdmx have been proposed: enhancing p53 ubiquitination by Mdm2 and inhibiting p53 activity. Here, we developed a mathematical model of the p53/Mdm2/Mdmx network to investigate which Mdmx functions quantitatively affect specific features of p53 dynamics under various conditions. We found that enhancement of Mdm2 activity was the most critical role of Mdmx under unstressed conditions. The model also accurately predicted p53 dynamics in Mdmx-depleted cells following DNA damage. This work outlines a strategy for rapidly testing possible network interactions to reveal those most impactful in regulating the dynamics of key proteins.